Quasi-periodic, sawtooth-like variations of energetic plasma particle fluxes are often measured at geosynchronous orbit during magnetic storms. The outstanding problems are whether the sawtooth flux variations represent particle injections from the tail to the inner magnetosphere, whether the sawtooth variations correspond to substorm onsets, and what mechanism is responsible for the generation of periodic particle injections (or periodic substorms). In this paper, we present the measurements of multiple space-based and ground-based instruments in the magnetosphere and ionosphere during two magnetic storms. The Geotail satellite was located in the near tail between XGSM = -20 and -30 RE and detected periodic southward turnings of the magnetospheric magnetic field. The southward turnings of Bz are interpreted as the signature of periodic near-tail reconnection and plasmoid formations. Geosynchronous satellites measured periodic gradual dropouts and rapid increases of energetic charged fluxes and magnetic field dipolarization. The IMAGE satellite measured enhanced emissions of energetic neutral atoms in the ring current and auroral brightenings. The Canadian Auroral Network for the OPEN Program Unified Study's photometers measured intensifications and latitudinal motion of auroral emissions. The auroral electrojet index showed periodic increases. These magnetospheric and ionospheric phenomena have the same periodicity and indicate the occurrence of periodic substorms. There is an excellent correspondence among the substorm signatures from all the measurements. The results show that periodic magnetospheric substorms can indeed occur during continuous southward interplanetary magnetic field, and the mean period in these two cases is ~2.7 hours. The sawtooth variations of energetic plasma fluxes at geosynchronous orbit represent true particle injections from the tail to the inner magnetosphere. The sawtooth injections are related to the near-tail reconnection and correspond to the onsets of periodic substorms.